To hotlink an image is to load it in an <img> tag from a source that didn't give you express permission to do so.
E.g.: If I were to post <img src="http://www.someguy.com/funnypic.jpg"> into a thread, without permission of someguy.com's owner, that's hotlinking. Every time someone loads the image, it costs someguy.com bandwidth. They're paying for your lulz. It's generally frowned upon.
To avoid hotlinking, either have your own server space you can use for hosting images, or host them on a site specifically created for that purpose. The downside to having your own server space is that you'll be the one paying for bandwidth. The downside to a third-party host is that you have to play by their rules, which usually means no nudity.
When Fark made changes to the user interface of the comments box, a new feature made it possible to upload photos from your computer directy to Fark's server. This eliminates problems with hotlinking to other websites. In 2015 this feature was also added to Fark mobile, making it easier to post selfies and other smartphone images.
Free image hosts include: